Generalised particle filters with Gaussian mixtures

Crisan, Dan; Li, Kai

doi:10.1016/j.spa.2015.01.008

Cited by 19 publications

(11 citation statements)

References 29 publications

(42 reference statements)

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“…A modern implementation of the particle filter to a high-dimensional filtering problem should involve intensive modifications to mitigate the curse of dimensionality. Successful innovations include proposal densities [34], mixtures [7], and dimension reduction strategies including the classic Rao-Blackwellized PF or recent localized PFs [24,25]. We conclude the numerics section by displaying the compatibility of Emu-PFs with a proposal density based PF, the Optimal Proposal PF, in section 4.7.…”

Section: 4mentioning

confidence: 97%

A surrogate-based approach to nonlinear, non-Gaussian joint state-parameter data assimilation

Maclean¹,

Spiller²

2021

FoDS

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<p style='text-indent:20px;'>Many recent advances in sequential assimilation of data into nonlinear high-dimensional models are modifications to particle filters which employ efficient searches of a high-dimensional state space. In this work, we present a complementary strategy that combines statistical emulators and particle filters. The emulators are used to learn and offer a computationally cheap approximation to the forward dynamic mapping. This emulator-particle filter (Emu-PF) approach requires a modest number of forward-model runs, but yields well-resolved posterior distributions even in non-Gaussian cases. We explore several modifications to the Emu-PF that utilize mechanisms for dimension reduction to efficiently fit the statistical emulator, and present a series of simulation experiments on an atypical Lorenz-96 system to demonstrate their performance. We conclude with a discussion on how the Emu-PF can be paired with modern particle filtering algorithms.</p>

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Section: 4mentioning

confidence: 97%

A surrogate-based approach to nonlinear, non-Gaussian joint state-parameter data assimilation

Maclean¹,

Spiller²

2021

FoDS

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“…This is equivalent to making a hard decision about the model in effect and hence the accuracy and precision of estimation is dependent on the correct choice of this model. At the cost of increased computational complexity, the performance of these methods can be improved by applying resampling procedures [16], [28], [39]. Alternatively, in [15], [21] a forgetting and merging algorithm is proposed, where the components with weights smaller than a given threshold are removed, and the components with close enough moments are merged.…”

Section: Introductionmentioning

confidence: 99%

Approximate MMSE Estimator for Linear Dynamic Systems With Gaussian Mixture Noise

Pishdad

Labeau

2017

IEEE Trans. Automat. Contr.

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Abstract-In this work we propose an approximate Minimum Mean-Square Error (MMSE) filter for linear dynamic systems with Gaussian Mixture noise. The proposed estimator tracks each component of the Gaussian Mixture (GM) posterior with an individual filter and minimizes the trace of the covariance matrix of the bank of filters, as opposed to minimizing the MSE of individual filters in the commonly used Gaussian sum filter (GSF). Hence, the spread of means in the proposed method is smaller than that of GSF which makes it more robust to removing components. Consequently, lower complexity reduction schemes can be used with the proposed filter without losing estimation accuracy and precision. This is supported through simulations on synthetic data as well as experimental data related to an indoor localization system. Additionally, we show that in two limit cases the state estimation provided by our proposed method converges to that of GSF, and we provide simulation results supporting this in other cases.

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“…Currently, most suboptimal methods for obtaining the posterior density in nonlinear discrete-time stochastic dynamic systems are using global and local approximation methods. Taking the point-mass filter based on adaptive algorithm [1] and particle filters with Gaussian mixtures based on Gaussian mixture approximation [2], for example, it is the advantage of the global approximate approach that any clear assumption pertaining to the form of posterior density is not needed. Although the global methods have strong adaptability, they suffer from enormous computational complexity.…”

Section: Introductionmentioning

confidence: 99%

Strong Tracking Filtering Algorithm of Randomly Delayed Measurements for Nonlinear Systems

Yang

Gao

Liu

2015

Mathematical Problems in Engineering

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This paper focuses on the filtering problems of nonlinear discrete-time stochastic dynamic systems, such as the model simplification, noise characteristics uncertainty, initial conditions uncertainty, or system parametric variation. Under these circumstances, the measurements of system have one sampling time random delay. A new method, that is, strong tracking filtering algorithm of randomly delayed measurements (STF/RDM) for nonlinear systems based on recursive operating by analytical computation and first-order linear approximations, is proposed; a principle of extended orthogonality is presented as a criterion of designing the STF/RDM, and through the residuals between available and predicted measurements, the formula of fading factor is obtained. Under the premise of using the extended orthogonality principle, STF/RDM proposed in this paper can adjust the fading factor online via calculating the covariance of residuals, and then the gain matrices of the STF/RDM adjust in real time to enhance the performance of the proposed method. Lastly, in order to prove that the performance of STF/RDM precedes existing EKF method, the experiment of tracking maneuvering aircraft is carried out.

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Generalised particle filters with Gaussian mixtures

Cited by 19 publications

References 29 publications

A surrogate-based approach to nonlinear, non-Gaussian joint state-parameter data assimilation

A surrogate-based approach to nonlinear, non-Gaussian joint state-parameter data assimilation

Approximate MMSE Estimator for Linear Dynamic Systems With Gaussian Mixture Noise

Strong Tracking Filtering Algorithm of Randomly Delayed Measurements for Nonlinear Systems

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